Jerusalem (CNN) -- Israel does not plan to extend a moratorium on settlement-building in the West Bank, Israeli Prime Minister Benjamin Netanyahu told party colleagues Sunday, despite a Palestinian threat to walk away from peace talks if building resumes.

U.S. Secretary of State Hillary Clinton is also pushing for a new three-month moratorium on Israeli building on land which the Palestinians consider theirs, a diplomatic source told CNN Thursday.

But Netanyahu told other leaders of his Likud party that there has been no change in Israel's position, sources familiar with the talks told CNN.

The settlement freeze is due to expire September 26.

The Palestinians have said that if the moratorium ends and building resumes they will walk away from peace talks, which recently resumed after an 18-month hiatus.

Clinton's proposal, which was made last week during Middle East peace talks being held in the region, was accepted by Palestinian Authority President Mahmoud Abbas, but essentially rejected by Netanyahu.

The two sides appear to be at a stalemate, the source said.

In an interview broadcast Sunday, Clinton said the U.S. goal was to keep the peace talks going.

"They need to keep talking," Clinton told the ABC program "This Week," later adding: "We don't want either party to leave the negotiations or to do anything that would cause the other party to leave the negotiations."

Netanyahu's official position remains that he will not support any extension of the moratorium, which has been in place for 10 months.

The U.S. special envoy to the region, former Sen. George Mitchell, is attempting to negotiate a "quid pro quo" from the Palestinians in exchange for an extension, the source added.

"There are all kinds of ideas in the air" over different ways to break the logjam, the source noted.

"Nobody is going to let the talks break down over this issue," the source said. "Nobody is walking out of these talks."

Among the ideas being discussed is a recognition on the part of the Palestinians of Israel as a fundamentally Jewish state.

A partial continuation of the moratorium is also under discussion, though Abbas has so far resisted anything less than a full extension, the source said.

Israeli and Palestinian negotiating teams are expected to continue discussing the issue at a meeting scheduled for Sunday, the source added.

The expectation is that some sort of solution will ultimately be found, the source said.